Using Desmos to find the quadratic model of a real-world image

Desmos is at it again...

Since I started using Desmos more regularly this summer, I have found that it is gradually replacing a number of my other math software options.  The latest instance happened when my algebra 2 students were finding examples of things that take the form of a parabola.

In the past, I have had students find an example of a parabola in their everyday lives and snap a picture of it.  I've seen images of everything from the McDonald's logo to a water fountain to a mug shot of someone's jaw line.  Then I would have students upload their images into Geometer's Sketchpad and construct a number of points along the parabola.  Here is an example...

After that, I would have the students enter the ordered pairs into a TI-84+ or TI-Nspire graphing calculator, find the regression equation, and go back to Sketchpad and graph the function on top of the image.  Again, an example:

Some years I would have students explore around with vertex form a bit to try to fit a quadratic model before we found the regression equation.  But it was a painfully long process to bounce back and forth between Sketchpad and graphing calculator.

This year, I decided to direct students to Desmos to compute the regression equation.  After all, we had used Desmos to find linear regression equations earlier in the year and all students had access to Desmos w/ our 1:1 laptops.  (Not all students would have a TI-84 or Nspire to use in years past.)

It turns out the students had a great idea. Why use Sketchpad to plot the points and graph the regression function?  Why not just use Desmos?  I loved the idea and it really simplified the process.

Students simply inserted their images into Desmos, plotted points on the parabola, created a table with their ordered pairs, and found the quadratic regression equation (& graph) all in one place.

Follow this link for an example (image shown below).

Better yet, using the sliders in Desmos is a breeze.  Simply insert an image of anything parabolic and have students fit the model using vertex form.

Growth Mindset & the Smarter Balanced Assessment

I was first exposed to Carol Dweck's research on fixed and growth mindsets a few years ago when I was completing some of my graduate coursework.  For those of you who haven't heard about mindsets, you can find a lot of resources online (here and here to name a few).

Dweck's colleague, Jo Boaler, has completed some further research on mindsets and the implications in the classroom.   If you're really interested in learning about mindsets in a mathematics classroom, I would recommend taking Stanford's free online class (sign up here).

In Dweck's Self-Theories book, she discusses the reaction of students with a helpless mindset (fixed mindset) when they experience failure.  In short, when a student with a fixed mindset experiences failure they begin to fall into a helpless state of mind.  They quickly lose confidence in their abilities and lose perspective on the successes they had achieved in the past.  Moreover, many students who had fallen into the helpless mindset "abandoned or became incapable of deploying the effective strategies in their repertoire." (pg. 9)

After hearing that research, I grew concerned about students who have a fixed mindset and their ability to successfully complete the Smarter Balanced assessment.  The Smarter Balanced Assessment is a computer adaptive test.  Students are given grade-level questions for the first two-thirds of the test.  Then the computer software selects remaining one-third of the questions based on the student responses up to that point.  If a student is answering questions correctly, then the software can select questions from a higher grade level.  Conversely, if a student is answering questions incorrectly, then the software can select questions from a lower grade level.

Theoretically, this type of testing system makes sense.  It's designed to find the "boundary" of each students' achievement level.  My concern lies with the students with fixed mindsets.  For those students, the "boundary" is like an electric fence.  The test is designed for students to eventually touch the fence.  Once a student with a fixed mindset does touch it, the electrical current sends shocks throughout their body.  They lose ability to focus on the problems and are more focused on how much the fence shocked them.

Dweck summarizes her research by saying "...the helpless response is a reaction to failure that carries negative implications for the self and that impairs students' ability to use their minds effectively."  I fear the computer adaptive test could indirectly lead to major negative consequences for students with a fixed mindset.

What can we (teachers) do to help?

I think the best way to help combat this potential problem is to teach students about fixed and growth mindsets.  I am planning to introduce these ideas during the first week of school in all of my classes.  More to come as to what that will look like...



Dweck, Carol S. Self-theories: Their Role in Motivation, Personality, and Development. Philadelphia, PA: Psychology, 1999. Print.

Student Created Videos

New year, new goals.

While doing some planning for our new semester, Mr. Huntimer found an activity on myOER that we decided to use to begin the second semester with our geometry classes.

Working in groups of two or three, students were given the task of finding real world objects that model a variety of 2-D and 3-D shapes.  Students were to either take a picture or a video clip of the object.  Then they were to create a video that fused all of the pictures or videos together.  As part of the video, students were required to define the object that they had found.

We allowed students to make a lot of decisions regarding their videos.  Students could define their objects using a number of different methods.  They could define objects as they recorded the video clips, they could record voice narration and align it to their pictures, or they could insert text into the video.  We had students use all three methods.

Students could create their videos around theme or concept.  We had one group use the theme of "shape hunters" and another use the theme of "mathletes".

We also allowed students to use whatever type of video editing software they'd like.  Our laptops have MovieMaker installed, so that served as our default video editor for those who had no preference.  Mr. Huntimer and I were rookies working with the software and found it very user friendly and easy to implement.  Some groups chose to use their iPhones and iMovie.  Another group used a third video editing software that we had never heard of before.  Our only stipulation was that students needed to submit their videos in mp4 or mov format so that we could view them from any computer (via Edmodo).

Overall, the task went very well.  We had some bumps in the road the first time through.  The biggest challenge was we had a number of groups submit their MovieMaker projects before they had converted them to mp4 format.  We simply had to ask those groups to convert and re-submit the videos.  A majority of the videos were similar in that they contained the minimum amount of effort / work needed to complete the task.  A few groups forgot to include all of the required information, thus costing them a few points.  Meanwhile, a few groups produced excellent videos that really caught our attention.

The content of the geometry in the task was really quite elementary, but the task did align to a CCSS ( G-MG.1).  The bigger skill that students practiced was collaboration and technology use.  We asked students to reflect on what they had learned in doing this project and many said they had never or rarely used software to create a video.  We were very happy with the technology application component.

I leave you with two links.  The first is a link to the task via myOER and Mr. Zachary Feldman (click here).

The second is a link to one of our best student videos.   The three gentlemen who created this video have agreed to share it.
Student Video

Technology & Computer Update

Sorry for the lack of updates... life is super busy for me right now.  My family and I recently moved into our new house.  We survived without internet at home for about 10 days.  It's tough to compose blog posts without access to the web.

Here's the latest on our computer and 1:1 situation...
We received the Dell laptops a couple of weeks ago.  As the tech department started imaging them, they noticed the styluses were not working with the machines.  To make a long story a little less long, the 60 Dell computers were packaged up and sent back to the supplier.

Needless to say, my colleague and I were not excited to wait and see what solution was going to be laid before us.  It turns out our technology department was working two bids for the laptops, so they immediately called the company with the "losing" bid.  They were able to ship us their product within and week and now we have the Lenovo Yoga laptop with stylus.  After being able to compare both computers, we are happy with the way things ended up.

The laptops are here, imaged, and in our classrooms.  The tech guys installed a wireless access point right in my room and signal strength is excellent.  Today we officially rolled the computers out to the students and completed our first homework assignment with the computers.

We have one final hurdle to clear.  Our 60 licenses for Geometer's Sketchpad are needing to be re-activated by KCP because we failed to de-authorize the computers that held the licenses last year.  After that, we hopefully should be fully ready to go.  Finally.

I've got another post coming in the near future.  I plan to talk about some of the hidden benefits of team teaching.  I will also posts some pics of the students and our computers.

Our computers have arrived!

We were delivered some exciting news today - our 60 laptop computers (w/ styluses) were delivered today.  Our tech department is in the process of imaging the machines and we should have them ready to go for next week!

In related news, our wireless network has been experiencing some serious problems these past two weeks.  Let's hope all the issues get resolved before our official roll-out.

Flexibility in Teaching

8 days until school starts...

It turns out our 60 laptops were ordered on August 8th, and we have not received them yet.  We may or may not get them in place before the first day of school.  This is very frustrating because we have already put in countless hours of planning and preparing to be able to use them extensively the first three days of school.

Here's to keeping our fingers crossed they arrive in the next few days and are able to be imaged and ready to go by next Tuesday.  And if not, this is just another example of teachers needing to be flexible in all they do.  Even the best laid plans are sometimes too simple.